Answer:
95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on LinkedIn is [0.081 , 0.279].
Step-by-step explanation:
We are given the data that shows the number of women and men who expressed that they trust recommendations made on LinkedIn in a recent survey;
Gender Women Men
Sample size 150 170
Trust Recommendations Made on LinkedIn 117 102
Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportions is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of women who trust recommendations made on LinkedIn = = 0.78
= sample proportion of men who trust recommendations made on LinkedIn = = 0.60
= sample of women = 150
= sample of men = 170
<em>Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.</em>
<u>So, 95% confidence interval for the difference between population proportions, (</u><u>) is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( < < ) = 0.95
P( < () < ) = 0.95
<u>95% confidence interval for</u> () =
[,]
= [ , ]
= [0.081 , 0.279]
Therefore, 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on LinkedIn is [0.081 , 0.279].